TSTP Solution File: SEU297+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU297+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:32:38 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 66
% Syntax : Number of formulae : 316 ( 63 unt; 0 def)
% Number of atoms : 1124 ( 71 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 1229 ( 421 ~; 457 |; 284 &)
% ( 21 <=>; 44 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 15 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 15 con; 0-3 aty)
% Number of variables : 406 ( 307 !; 99 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f497,plain,
$false,
inference(avatar_sat_refutation,[],[f234,f255,f283,f333,f342,f345,f418,f420,f434,f455,f467,f477,f496]) ).
fof(f496,plain,
( ~ spl26_8
| ~ spl26_10
| ~ spl26_12
| ~ spl26_14 ),
inference(avatar_contradiction_clause,[],[f495]) ).
fof(f495,plain,
( $false
| ~ spl26_8
| ~ spl26_10
| ~ spl26_12
| ~ spl26_14 ),
inference(subsumption_resolution,[],[f494,f417]) ).
fof(f417,plain,
( in(sK4(sK12(sK2,sK3)),sK12(sK2,sK3))
| ~ spl26_10 ),
inference(avatar_component_clause,[],[f415]) ).
fof(f415,plain,
( spl26_10
<=> in(sK4(sK12(sK2,sK3)),sK12(sK2,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_10])]) ).
fof(f494,plain,
( ~ in(sK4(sK12(sK2,sK3)),sK12(sK2,sK3))
| ~ spl26_8
| ~ spl26_12
| ~ spl26_14 ),
inference(subsumption_resolution,[],[f492,f332]) ).
fof(f332,plain,
( in(relation_image(sK3,sK4(sK12(sK2,sK3))),sK2)
| ~ spl26_8 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f330,plain,
( spl26_8
<=> in(relation_image(sK3,sK4(sK12(sK2,sK3))),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_8])]) ).
fof(f492,plain,
( ~ in(relation_image(sK3,sK4(sK12(sK2,sK3))),sK2)
| ~ in(sK4(sK12(sK2,sK3)),sK12(sK2,sK3))
| ~ spl26_12
| ~ spl26_14 ),
inference(resolution,[],[f479,f125]) ).
fof(f125,plain,
! [X3] :
( ~ in(sK4(X3),powerset(relation_dom(sK3)))
| ~ in(relation_image(sK3,sK4(X3)),sK2)
| ~ in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
( ! [X3] :
( ( ~ in(relation_image(sK3,sK4(X3)),sK2)
| ~ in(sK4(X3),powerset(relation_dom(sK3)))
| ~ in(sK4(X3),X3) )
& ( ( in(relation_image(sK3,sK4(X3)),sK2)
& in(sK4(X3),powerset(relation_dom(sK3))) )
| in(sK4(X3),X3) ) )
& function(sK3)
& relation(sK3)
& element(sK2,powerset(powerset(sK1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f75,f77,f76]) ).
fof(f76,plain,
( ? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ~ in(relation_image(X2,X4),X1)
| ~ in(X4,powerset(relation_dom(X2)))
| ~ in(X4,X3) )
& ( ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) )
| in(X4,X3) ) )
& function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0))) )
=> ( ! [X3] :
? [X4] :
( ( ~ in(relation_image(sK3,X4),sK2)
| ~ in(X4,powerset(relation_dom(sK3)))
| ~ in(X4,X3) )
& ( ( in(relation_image(sK3,X4),sK2)
& in(X4,powerset(relation_dom(sK3))) )
| in(X4,X3) ) )
& function(sK3)
& relation(sK3)
& element(sK2,powerset(powerset(sK1))) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X3] :
( ? [X4] :
( ( ~ in(relation_image(sK3,X4),sK2)
| ~ in(X4,powerset(relation_dom(sK3)))
| ~ in(X4,X3) )
& ( ( in(relation_image(sK3,X4),sK2)
& in(X4,powerset(relation_dom(sK3))) )
| in(X4,X3) ) )
=> ( ( ~ in(relation_image(sK3,sK4(X3)),sK2)
| ~ in(sK4(X3),powerset(relation_dom(sK3)))
| ~ in(sK4(X3),X3) )
& ( ( in(relation_image(sK3,sK4(X3)),sK2)
& in(sK4(X3),powerset(relation_dom(sK3))) )
| in(sK4(X3),X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ~ in(relation_image(X2,X4),X1)
| ~ in(X4,powerset(relation_dom(X2)))
| ~ in(X4,X3) )
& ( ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) )
| in(X4,X3) ) )
& function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ~ in(relation_image(X2,X4),X1)
| ~ in(X4,powerset(relation_dom(X2)))
| ~ in(X4,X3) )
& ( ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) )
| in(X4,X3) ) )
& function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0))) ),
inference(nnf_transformation,[],[f48]) ).
fof(f48,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( in(X4,X3)
<~> ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) ) )
& function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f47]) ).
fof(f47,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( in(X4,X3)
<~> ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) ) )
& function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0))) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0))) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_27__finset_1) ).
fof(f479,plain,
( in(sK4(sK12(sK2,sK3)),powerset(relation_dom(sK3)))
| ~ spl26_12
| ~ spl26_14 ),
inference(superposition,[],[f454,f476]) ).
fof(f476,plain,
( sK4(sK12(sK2,sK3)) = sK13(sK2,sK3,sK4(sK12(sK2,sK3)))
| ~ spl26_14 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f474,plain,
( spl26_14
<=> sK4(sK12(sK2,sK3)) = sK13(sK2,sK3,sK4(sK12(sK2,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_14])]) ).
fof(f454,plain,
( in(sK13(sK2,sK3,sK4(sK12(sK2,sK3))),powerset(relation_dom(sK3)))
| ~ spl26_12 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f452,plain,
( spl26_12
<=> in(sK13(sK2,sK3,sK4(sK12(sK2,sK3))),powerset(relation_dom(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_12])]) ).
fof(f477,plain,
( spl26_9
| spl26_14
| spl26_7
| ~ spl26_10 ),
inference(avatar_split_clause,[],[f430,f415,f326,f474,f412]) ).
fof(f412,plain,
( spl26_9
<=> ! [X0] : ~ element(sK2,powerset(powerset(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_9])]) ).
fof(f326,plain,
( spl26_7
<=> sP0(sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_7])]) ).
fof(f430,plain,
( ! [X0] :
( sK4(sK12(sK2,sK3)) = sK13(sK2,sK3,sK4(sK12(sK2,sK3)))
| ~ element(sK2,powerset(powerset(X0))) )
| spl26_7
| ~ spl26_10 ),
inference(subsumption_resolution,[],[f429,f121]) ).
fof(f121,plain,
relation(sK3),
inference(cnf_transformation,[],[f78]) ).
fof(f429,plain,
( ! [X0] :
( sK4(sK12(sK2,sK3)) = sK13(sK2,sK3,sK4(sK12(sK2,sK3)))
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X0))) )
| spl26_7
| ~ spl26_10 ),
inference(subsumption_resolution,[],[f428,f122]) ).
fof(f122,plain,
function(sK3),
inference(cnf_transformation,[],[f78]) ).
fof(f428,plain,
( ! [X0] :
( sK4(sK12(sK2,sK3)) = sK13(sK2,sK3,sK4(sK12(sK2,sK3)))
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X0))) )
| spl26_7
| ~ spl26_10 ),
inference(subsumption_resolution,[],[f422,f327]) ).
fof(f327,plain,
( ~ sP0(sK2,sK3)
| spl26_7 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f422,plain,
( ! [X0] :
( sK4(sK12(sK2,sK3)) = sK13(sK2,sK3,sK4(sK12(sK2,sK3)))
| sP0(sK2,sK3)
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X0))) )
| ~ spl26_10 ),
inference(resolution,[],[f417,f171]) ).
fof(f171,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK12(X1,X2))
| sK13(X1,X2,X4) = X4
| sP0(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ! [X4] :
( ( in(X4,sK12(X1,X2))
| ! [X5] :
( ~ in(relation_image(X2,X4),X1)
| X4 != X5
| ~ in(X5,powerset(relation_dom(X2))) ) )
& ( ( in(relation_image(X2,X4),X1)
& sK13(X1,X2,X4) = X4
& in(sK13(X1,X2,X4),powerset(relation_dom(X2))) )
| ~ in(X4,sK12(X1,X2)) ) )
| sP0(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f92,f94,f93]) ).
fof(f93,plain,
! [X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5] :
( ~ in(relation_image(X2,X4),X1)
| X4 != X5
| ~ in(X5,powerset(relation_dom(X2))) ) )
& ( ? [X6] :
( in(relation_image(X2,X4),X1)
& X4 = X6
& in(X6,powerset(relation_dom(X2))) )
| ~ in(X4,X3) ) )
=> ! [X4] :
( ( in(X4,sK12(X1,X2))
| ! [X5] :
( ~ in(relation_image(X2,X4),X1)
| X4 != X5
| ~ in(X5,powerset(relation_dom(X2))) ) )
& ( ? [X6] :
( in(relation_image(X2,X4),X1)
& X4 = X6
& in(X6,powerset(relation_dom(X2))) )
| ~ in(X4,sK12(X1,X2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
! [X1,X2,X4] :
( ? [X6] :
( in(relation_image(X2,X4),X1)
& X4 = X6
& in(X6,powerset(relation_dom(X2))) )
=> ( in(relation_image(X2,X4),X1)
& sK13(X1,X2,X4) = X4
& in(sK13(X1,X2,X4),powerset(relation_dom(X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5] :
( ~ in(relation_image(X2,X4),X1)
| X4 != X5
| ~ in(X5,powerset(relation_dom(X2))) ) )
& ( ? [X6] :
( in(relation_image(X2,X4),X1)
& X4 = X6
& in(X6,powerset(relation_dom(X2))) )
| ~ in(X4,X3) ) )
| sP0(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0))) ),
inference(rectify,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ? [X6] :
! [X7] :
( ( in(X7,X6)
| ! [X8] :
( ~ in(relation_image(X2,X7),X1)
| X7 != X8
| ~ in(X8,powerset(relation_dom(X2))) ) )
& ( ? [X8] :
( in(relation_image(X2,X7),X1)
& X7 = X8
& in(X8,powerset(relation_dom(X2))) )
| ~ in(X7,X6) ) )
| sP0(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0))) ),
inference(nnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(relation_image(X2,X7),X1)
& X7 = X8
& in(X8,powerset(relation_dom(X2))) ) )
| sP0(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0))) ),
inference(definition_folding,[],[f71,f72]) ).
fof(f72,plain,
! [X1,X2] :
( ? [X3,X4,X5] :
( X4 != X5
& in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4 )
| ~ sP0(X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(relation_image(X2,X7),X1)
& X7 = X8
& in(X8,powerset(relation_dom(X2))) ) )
| ? [X3,X4,X5] :
( X4 != X5
& in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(relation_image(X2,X7),X1)
& X7 = X8
& in(X8,powerset(relation_dom(X2))) ) )
| ? [X3,X4,X5] :
( X4 != X5
& in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0))) )
=> ( ! [X3,X4,X5] :
( ( in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4 )
=> X4 = X5 )
=> ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(relation_image(X2,X7),X1)
& X7 = X8
& in(X8,powerset(relation_dom(X2))) ) ) ) ),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0))) )
=> ( ! [X3,X4,X5] :
( ( in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4 )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(relation_image(X2,X4),X1)
& X4 = X5
& in(X5,powerset(relation_dom(X2))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_27__finset_1__1) ).
fof(f467,plain,
( spl26_9
| spl26_13
| spl26_7
| ~ spl26_11 ),
inference(avatar_split_clause,[],[f450,f432,f326,f465,f412]) ).
fof(f465,plain,
( spl26_13
<=> ! [X0] :
( in(sK4(X0),X0)
| sK4(X0) = sK13(sK2,sK3,sK4(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_13])]) ).
fof(f432,plain,
( spl26_11
<=> ! [X0] :
( in(sK4(X0),sK12(sK2,sK3))
| in(sK4(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_11])]) ).
fof(f450,plain,
( ! [X0,X1] :
( in(sK4(X0),X0)
| sK4(X0) = sK13(sK2,sK3,sK4(X0))
| ~ element(sK2,powerset(powerset(X1))) )
| spl26_7
| ~ spl26_11 ),
inference(subsumption_resolution,[],[f449,f121]) ).
fof(f449,plain,
( ! [X0,X1] :
( in(sK4(X0),X0)
| sK4(X0) = sK13(sK2,sK3,sK4(X0))
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X1))) )
| spl26_7
| ~ spl26_11 ),
inference(subsumption_resolution,[],[f448,f122]) ).
fof(f448,plain,
( ! [X0,X1] :
( in(sK4(X0),X0)
| sK4(X0) = sK13(sK2,sK3,sK4(X0))
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X1))) )
| spl26_7
| ~ spl26_11 ),
inference(subsumption_resolution,[],[f436,f327]) ).
fof(f436,plain,
( ! [X0,X1] :
( in(sK4(X0),X0)
| sK4(X0) = sK13(sK2,sK3,sK4(X0))
| sP0(sK2,sK3)
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X1))) )
| ~ spl26_11 ),
inference(resolution,[],[f433,f171]) ).
fof(f433,plain,
( ! [X0] :
( in(sK4(X0),sK12(sK2,sK3))
| in(sK4(X0),X0) )
| ~ spl26_11 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f455,plain,
( spl26_9
| spl26_12
| spl26_7
| ~ spl26_10 ),
inference(avatar_split_clause,[],[f427,f415,f326,f452,f412]) ).
fof(f427,plain,
( ! [X0] :
( in(sK13(sK2,sK3,sK4(sK12(sK2,sK3))),powerset(relation_dom(sK3)))
| ~ element(sK2,powerset(powerset(X0))) )
| spl26_7
| ~ spl26_10 ),
inference(subsumption_resolution,[],[f426,f121]) ).
fof(f426,plain,
( ! [X0] :
( in(sK13(sK2,sK3,sK4(sK12(sK2,sK3))),powerset(relation_dom(sK3)))
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X0))) )
| spl26_7
| ~ spl26_10 ),
inference(subsumption_resolution,[],[f425,f122]) ).
fof(f425,plain,
( ! [X0] :
( in(sK13(sK2,sK3,sK4(sK12(sK2,sK3))),powerset(relation_dom(sK3)))
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X0))) )
| spl26_7
| ~ spl26_10 ),
inference(subsumption_resolution,[],[f421,f327]) ).
fof(f421,plain,
( ! [X0] :
( in(sK13(sK2,sK3,sK4(sK12(sK2,sK3))),powerset(relation_dom(sK3)))
| sP0(sK2,sK3)
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X0))) )
| ~ spl26_10 ),
inference(resolution,[],[f417,f170]) ).
fof(f170,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK12(X1,X2))
| in(sK13(X1,X2,X4),powerset(relation_dom(X2)))
| sP0(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f434,plain,
( spl26_9
| spl26_11
| spl26_7 ),
inference(avatar_split_clause,[],[f402,f326,f432,f412]) ).
fof(f402,plain,
( ! [X0,X1] :
( in(sK4(X0),sK12(sK2,sK3))
| ~ element(sK2,powerset(powerset(X1)))
| in(sK4(X0),X0) )
| spl26_7 ),
inference(subsumption_resolution,[],[f401,f123]) ).
fof(f123,plain,
! [X3] :
( in(sK4(X3),powerset(relation_dom(sK3)))
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f78]) ).
fof(f401,plain,
( ! [X0,X1] :
( in(sK4(X0),sK12(sK2,sK3))
| ~ in(sK4(X0),powerset(relation_dom(sK3)))
| ~ element(sK2,powerset(powerset(X1)))
| in(sK4(X0),X0) )
| spl26_7 ),
inference(subsumption_resolution,[],[f400,f121]) ).
fof(f400,plain,
( ! [X0,X1] :
( in(sK4(X0),sK12(sK2,sK3))
| ~ in(sK4(X0),powerset(relation_dom(sK3)))
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X1)))
| in(sK4(X0),X0) )
| spl26_7 ),
inference(subsumption_resolution,[],[f399,f122]) ).
fof(f399,plain,
( ! [X0,X1] :
( in(sK4(X0),sK12(sK2,sK3))
| ~ in(sK4(X0),powerset(relation_dom(sK3)))
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X1)))
| in(sK4(X0),X0) )
| spl26_7 ),
inference(subsumption_resolution,[],[f382,f327]) ).
fof(f382,plain,
! [X0,X1] :
( in(sK4(X0),sK12(sK2,sK3))
| ~ in(sK4(X0),powerset(relation_dom(sK3)))
| sP0(sK2,sK3)
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X1)))
| in(sK4(X0),X0) ),
inference(resolution,[],[f206,f124]) ).
fof(f124,plain,
! [X3] :
( in(relation_image(sK3,sK4(X3)),sK2)
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f78]) ).
fof(f206,plain,
! [X2,X0,X1,X5] :
( ~ in(relation_image(X2,X5),X1)
| in(X5,sK12(X1,X2))
| ~ in(X5,powerset(relation_dom(X2)))
| sP0(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0))) ),
inference(equality_resolution,[],[f173]) ).
fof(f173,plain,
! [X2,X0,X1,X4,X5] :
( in(X4,sK12(X1,X2))
| ~ in(relation_image(X2,X4),X1)
| X4 != X5
| ~ in(X5,powerset(relation_dom(X2)))
| sP0(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f420,plain,
~ spl26_9,
inference(avatar_contradiction_clause,[],[f419]) ).
fof(f419,plain,
( $false
| ~ spl26_9 ),
inference(resolution,[],[f413,f120]) ).
fof(f120,plain,
element(sK2,powerset(powerset(sK1))),
inference(cnf_transformation,[],[f78]) ).
fof(f413,plain,
( ! [X0] : ~ element(sK2,powerset(powerset(X0)))
| ~ spl26_9 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f418,plain,
( spl26_9
| spl26_10
| spl26_7
| ~ spl26_8 ),
inference(avatar_split_clause,[],[f410,f330,f326,f415,f412]) ).
fof(f410,plain,
( ! [X0] :
( in(sK4(sK12(sK2,sK3)),sK12(sK2,sK3))
| ~ element(sK2,powerset(powerset(X0))) )
| spl26_7
| ~ spl26_8 ),
inference(subsumption_resolution,[],[f409,f123]) ).
fof(f409,plain,
( ! [X0] :
( in(sK4(sK12(sK2,sK3)),sK12(sK2,sK3))
| ~ in(sK4(sK12(sK2,sK3)),powerset(relation_dom(sK3)))
| ~ element(sK2,powerset(powerset(X0))) )
| spl26_7
| ~ spl26_8 ),
inference(subsumption_resolution,[],[f408,f121]) ).
fof(f408,plain,
( ! [X0] :
( in(sK4(sK12(sK2,sK3)),sK12(sK2,sK3))
| ~ in(sK4(sK12(sK2,sK3)),powerset(relation_dom(sK3)))
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X0))) )
| spl26_7
| ~ spl26_8 ),
inference(subsumption_resolution,[],[f407,f122]) ).
fof(f407,plain,
( ! [X0] :
( in(sK4(sK12(sK2,sK3)),sK12(sK2,sK3))
| ~ in(sK4(sK12(sK2,sK3)),powerset(relation_dom(sK3)))
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X0))) )
| spl26_7
| ~ spl26_8 ),
inference(subsumption_resolution,[],[f384,f327]) ).
fof(f384,plain,
( ! [X0] :
( in(sK4(sK12(sK2,sK3)),sK12(sK2,sK3))
| ~ in(sK4(sK12(sK2,sK3)),powerset(relation_dom(sK3)))
| sP0(sK2,sK3)
| ~ function(sK3)
| ~ relation(sK3)
| ~ element(sK2,powerset(powerset(X0))) )
| ~ spl26_8 ),
inference(resolution,[],[f206,f332]) ).
fof(f345,plain,
~ spl26_7,
inference(avatar_contradiction_clause,[],[f344]) ).
fof(f344,plain,
( $false
| ~ spl26_7 ),
inference(global_subsumption,[],[f206,f170,f121,f122,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f192,f193,f194,f195,f196,f197,f198,f199,f200,f201,f202,f203,f204,f205,f126,f154,f156,f157,f158,f159,f160,f161,f162,f120,f138,f139,f209,f210,f207,f140,f215,f213,f141,f142,f143,f128,f130,f131,f144,f219,f145,f153,f155,f220,f147,f163,f127,f129,f135,f221,f136,f224,f241,f137,f261,f146,f123,f266,f267,f124,f264,f265,f268,f269,f132,f270,f273,f271,f222,f164,f223,f239,f240,f259,f260,f243,f245,f165,f166,f167,f168,f169,f295,f296,f286,f288,f290,f292,f125,f303,f172,f306,f307,f308,f305,f314,f315,f312,f313,f309,f316,f317,f171,f321,f322,f323,f324,f320,f328,f335,f334,f339,f340,f343]) ).
fof(f343,plain,
( in(relation_image(sK3,sK9(sK2,sK3)),sK2)
| ~ spl26_7 ),
inference(subsumption_resolution,[],[f338,f328]) ).
fof(f338,plain,
( in(relation_image(sK3,sK9(sK2,sK3)),sK2)
| ~ sP0(sK2,sK3)
| ~ spl26_7 ),
inference(superposition,[],[f168,f334]) ).
fof(f340,plain,
( sK9(sK2,sK3) != sK10(sK2,sK3)
| ~ spl26_7 ),
inference(subsumption_resolution,[],[f337,f328]) ).
fof(f337,plain,
( sK9(sK2,sK3) != sK10(sK2,sK3)
| ~ sP0(sK2,sK3)
| ~ spl26_7 ),
inference(superposition,[],[f169,f334]) ).
fof(f339,plain,
( ~ in(sK2,relation_image(sK3,sK9(sK2,sK3)))
| ~ spl26_7 ),
inference(subsumption_resolution,[],[f336,f328]) ).
fof(f336,plain,
( ~ in(sK2,relation_image(sK3,sK9(sK2,sK3)))
| ~ sP0(sK2,sK3)
| ~ spl26_7 ),
inference(superposition,[],[f296,f334]) ).
fof(f334,plain,
( sK9(sK2,sK3) = sK11(sK2,sK3)
| ~ spl26_7 ),
inference(resolution,[],[f328,f167]) ).
fof(f335,plain,
( sK9(sK2,sK3) = sK10(sK2,sK3)
| ~ spl26_7 ),
inference(resolution,[],[f328,f165]) ).
fof(f328,plain,
( sP0(sK2,sK3)
| ~ spl26_7 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f320,plain,
( in(relation_image(sK3,sK4(sK12(sK2,sK3))),sK2)
| sP0(sK2,sK3) ),
inference(subsumption_resolution,[],[f319,f122]) ).
fof(f319,plain,
( in(relation_image(sK3,sK4(sK12(sK2,sK3))),sK2)
| ~ function(sK3)
| sP0(sK2,sK3) ),
inference(subsumption_resolution,[],[f318,f121]) ).
fof(f318,plain,
( in(relation_image(sK3,sK4(sK12(sK2,sK3))),sK2)
| ~ relation(sK3)
| ~ function(sK3)
| sP0(sK2,sK3) ),
inference(factoring,[],[f309]) ).
fof(f324,plain,
! [X2,X3,X0,X1] :
( relation_image(X2,sK11(sK12(X0,X1),X2)) = sK13(X0,X1,relation_image(X2,sK11(sK12(X0,X1),X2)))
| sP0(X0,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X0,powerset(powerset(X3)))
| ~ sP0(sK12(X0,X1),X2) ),
inference(resolution,[],[f171,f168]) ).
fof(f323,plain,
! [X2,X3,X0,X1] :
( relation_image(X2,sK10(sK12(X0,X1),X2)) = sK13(X0,X1,relation_image(X2,sK10(sK12(X0,X1),X2)))
| sP0(X0,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X0,powerset(powerset(X3)))
| ~ sP0(sK12(X0,X1),X2) ),
inference(resolution,[],[f171,f166]) ).
fof(f322,plain,
! [X2,X0,X1] :
( sK4(sK12(X0,X1)) = sK13(X0,X1,sK4(sK12(X0,X1)))
| sP0(X0,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X0,powerset(powerset(X2)))
| in(sK4(sK12(X0,X1)),powerset(relation_dom(sK3))) ),
inference(resolution,[],[f171,f123]) ).
fof(f321,plain,
! [X2,X0,X1] :
( ~ element(X0,powerset(powerset(X2)))
| sP0(X0,X1)
| ~ function(X1)
| ~ relation(X1)
| sK4(sK12(X0,X1)) = sK13(X0,X1,sK4(sK12(X0,X1)))
| in(relation_image(sK3,sK4(sK12(X0,X1))),sK2) ),
inference(resolution,[],[f171,f124]) ).
fof(f317,plain,
! [X0] :
( ~ in(sK2,relation_image(X0,sK4(sK12(sK2,X0))))
| ~ relation(X0)
| ~ function(X0)
| sP0(sK2,X0)
| in(relation_image(sK3,sK4(sK12(sK2,X0))),sK2) ),
inference(resolution,[],[f309,f163]) ).
fof(f316,plain,
! [X0] :
( in(relation_image(X0,sK4(sK12(sK2,X0))),sK2)
| ~ relation(X0)
| ~ function(X0)
| sP0(sK2,X0)
| ~ in(sK2,relation_image(sK3,sK4(sK12(sK2,X0)))) ),
inference(resolution,[],[f309,f163]) ).
fof(f309,plain,
! [X0] :
( in(relation_image(sK3,sK4(sK12(sK2,X0))),sK2)
| in(relation_image(X0,sK4(sK12(sK2,X0))),sK2)
| ~ relation(X0)
| ~ function(X0)
| sP0(sK2,X0) ),
inference(resolution,[],[f305,f120]) ).
fof(f313,plain,
! [X0,X1] :
( in(relation_image(X1,sK4(sK12(sK8(powerset(X0)),X1))),sK8(powerset(X0)))
| ~ function(X1)
| ~ relation(X1)
| sP0(sK8(powerset(X0)),X1)
| in(relation_image(sK3,sK4(sK12(sK8(powerset(X0)),X1))),sK2) ),
inference(resolution,[],[f305,f155]) ).
fof(f312,plain,
! [X0,X1] :
( in(relation_image(X1,sK4(sK12(sK7(powerset(X0)),X1))),sK7(powerset(X0)))
| ~ function(X1)
| ~ relation(X1)
| sP0(sK7(powerset(X0)),X1)
| in(relation_image(sK3,sK4(sK12(sK7(powerset(X0)),X1))),sK2) ),
inference(resolution,[],[f305,f153]) ).
fof(f315,plain,
! [X0,X1] :
( in(relation_image(X1,sK4(sK12(sK6(powerset(X0)),X1))),sK6(powerset(X0)))
| ~ function(X1)
| ~ relation(X1)
| sP0(sK6(powerset(X0)),X1)
| in(relation_image(sK3,sK4(sK12(sK6(powerset(X0)),X1))),sK2) ),
inference(subsumption_resolution,[],[f311,f126]) ).
fof(f311,plain,
! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| ~ function(X1)
| ~ relation(X1)
| in(relation_image(X1,sK4(sK12(sK6(powerset(X0)),X1))),sK6(powerset(X0)))
| in(relation_image(sK3,sK4(sK12(sK6(powerset(X0)),X1))),sK2)
| empty(powerset(X0)) ),
inference(resolution,[],[f305,f129]) ).
fof(f314,plain,
! [X0,X1] :
( in(relation_image(X1,sK4(sK12(sK5(powerset(X0)),X1))),sK5(powerset(X0)))
| ~ function(X1)
| ~ relation(X1)
| sP0(sK5(powerset(X0)),X1)
| in(relation_image(sK3,sK4(sK12(sK5(powerset(X0)),X1))),sK2) ),
inference(subsumption_resolution,[],[f310,f126]) ).
fof(f310,plain,
! [X0,X1] :
( sP0(sK5(powerset(X0)),X1)
| ~ function(X1)
| ~ relation(X1)
| in(relation_image(X1,sK4(sK12(sK5(powerset(X0)),X1))),sK5(powerset(X0)))
| in(relation_image(sK3,sK4(sK12(sK5(powerset(X0)),X1))),sK2)
| empty(powerset(X0)) ),
inference(resolution,[],[f305,f127]) ).
fof(f305,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(powerset(X2)))
| sP0(X1,X0)
| ~ function(X0)
| ~ relation(X0)
| in(relation_image(X0,sK4(sK12(X1,X0))),X1)
| in(relation_image(sK3,sK4(sK12(X1,X0))),sK2) ),
inference(resolution,[],[f172,f124]) ).
fof(f308,plain,
! [X2,X3,X0,X1] :
( in(relation_image(X0,relation_image(X1,sK11(sK12(X2,X0),X1))),X2)
| sP0(X2,X0)
| ~ function(X0)
| ~ relation(X0)
| ~ element(X2,powerset(powerset(X3)))
| ~ sP0(sK12(X2,X0),X1) ),
inference(resolution,[],[f172,f168]) ).
fof(f307,plain,
! [X2,X3,X0,X1] :
( in(relation_image(X0,relation_image(X1,sK10(sK12(X2,X0),X1))),X2)
| sP0(X2,X0)
| ~ function(X0)
| ~ relation(X0)
| ~ element(X2,powerset(powerset(X3)))
| ~ sP0(sK12(X2,X0),X1) ),
inference(resolution,[],[f172,f166]) ).
fof(f306,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(powerset(X2)))
| sP0(X1,X0)
| ~ function(X0)
| ~ relation(X0)
| in(relation_image(X0,sK4(sK12(X1,X0))),X1)
| in(sK4(sK12(X1,X0)),powerset(relation_dom(sK3))) ),
inference(resolution,[],[f172,f123]) ).
fof(f172,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK12(X1,X2))
| in(relation_image(X2,X4),X1)
| sP0(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f303,plain,
~ in(relation_image(sK3,sK4(powerset(relation_dom(sK3)))),sK2),
inference(subsumption_resolution,[],[f302,f266]) ).
fof(f302,plain,
( ~ in(relation_image(sK3,sK4(powerset(relation_dom(sK3)))),sK2)
| ~ in(sK4(powerset(relation_dom(sK3))),powerset(relation_dom(sK3))) ),
inference(resolution,[],[f125,f266]) ).
fof(f292,plain,
! [X0] :
( epsilon_connected(sK6(X0))
| empty(X0)
| ~ epsilon_connected(powerset(X0))
| ~ epsilon_transitive(powerset(X0)) ),
inference(resolution,[],[f240,f147]) ).
fof(f290,plain,
! [X0] :
( epsilon_connected(sK5(X0))
| empty(X0)
| ~ epsilon_connected(powerset(X0))
| ~ epsilon_transitive(powerset(X0)) ),
inference(resolution,[],[f239,f147]) ).
fof(f288,plain,
! [X0] :
( ~ epsilon_connected(powerset(X0))
| empty(X0)
| epsilon_transitive(sK6(X0))
| ~ epsilon_transitive(powerset(X0)) ),
inference(resolution,[],[f223,f147]) ).
fof(f286,plain,
! [X0] :
( ~ epsilon_connected(powerset(X0))
| empty(X0)
| epsilon_transitive(sK5(X0))
| ~ epsilon_transitive(powerset(X0)) ),
inference(resolution,[],[f222,f147]) ).
fof(f296,plain,
! [X0,X1] :
( ~ in(X0,relation_image(X1,sK11(X0,X1)))
| ~ sP0(X0,X1) ),
inference(resolution,[],[f168,f163]) ).
fof(f295,plain,
! [X0,X1] :
( ~ in(X0,relation_image(X1,sK10(X0,X1)))
| ~ sP0(X0,X1) ),
inference(resolution,[],[f166,f163]) ).
fof(f169,plain,
! [X0,X1] :
( sK10(X0,X1) != sK11(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( ( sK10(X0,X1) != sK11(X0,X1)
& in(relation_image(X1,sK11(X0,X1)),X0)
& sK9(X0,X1) = sK11(X0,X1)
& in(relation_image(X1,sK10(X0,X1)),X0)
& sK9(X0,X1) = sK10(X0,X1) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f88,f89]) ).
fof(f89,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& in(relation_image(X1,X4),X0)
& X2 = X4
& in(relation_image(X1,X3),X0)
& X2 = X3 )
=> ( sK10(X0,X1) != sK11(X0,X1)
& in(relation_image(X1,sK11(X0,X1)),X0)
& sK9(X0,X1) = sK11(X0,X1)
& in(relation_image(X1,sK10(X0,X1)),X0)
& sK9(X0,X1) = sK10(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& in(relation_image(X1,X4),X0)
& X2 = X4
& in(relation_image(X1,X3),X0)
& X2 = X3 )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f87]) ).
fof(f87,plain,
! [X1,X2] :
( ? [X3,X4,X5] :
( X4 != X5
& in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4 )
| ~ sP0(X1,X2) ),
inference(nnf_transformation,[],[f72]) ).
fof(f168,plain,
! [X0,X1] :
( in(relation_image(X1,sK11(X0,X1)),X0)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f167,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK9(X0,X1) = sK11(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f166,plain,
! [X0,X1] :
( in(relation_image(X1,sK10(X0,X1)),X0)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f165,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK9(X0,X1) = sK10(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f245,plain,
! [X0] :
( epsilon_connected(sK7(X0))
| ~ epsilon_connected(powerset(X0))
| ~ epsilon_transitive(powerset(X0)) ),
inference(resolution,[],[f241,f147]) ).
fof(f243,plain,
! [X0] :
( ~ epsilon_connected(powerset(X0))
| epsilon_transitive(sK7(X0))
| ~ epsilon_transitive(powerset(X0)) ),
inference(resolution,[],[f224,f147]) ).
fof(f260,plain,
! [X0] :
( ordinal(sK6(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ),
inference(resolution,[],[f137,f129]) ).
fof(f259,plain,
! [X0] :
( ordinal(sK5(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ),
inference(resolution,[],[f137,f127]) ).
fof(f240,plain,
! [X0] :
( ~ ordinal(powerset(X0))
| epsilon_connected(sK6(X0))
| empty(X0) ),
inference(resolution,[],[f136,f129]) ).
fof(f239,plain,
! [X0] :
( ~ ordinal(powerset(X0))
| epsilon_connected(sK5(X0))
| empty(X0) ),
inference(resolution,[],[f136,f127]) ).
fof(f223,plain,
! [X0] :
( ~ ordinal(powerset(X0))
| epsilon_transitive(sK6(X0))
| empty(X0) ),
inference(resolution,[],[f135,f129]) ).
fof(f164,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( ( finite(X1)
& function(X0)
& relation(X0) )
=> finite(relation_image(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).
fof(f222,plain,
! [X0] :
( ~ ordinal(powerset(X0))
| epsilon_transitive(sK5(X0))
| empty(X0) ),
inference(resolution,[],[f135,f127]) ).
fof(f271,plain,
! [X0] :
( finite(sK5(X0))
| ~ finite(X0)
| empty(X0) ),
inference(resolution,[],[f132,f127]) ).
fof(f273,plain,
! [X0] :
( finite(sK7(X0))
| ~ finite(X0) ),
inference(resolution,[],[f132,f153]) ).
fof(f270,plain,
( finite(sK2)
| ~ finite(powerset(sK1)) ),
inference(resolution,[],[f132,f120]) ).
fof(f132,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( finite(X1)
| ~ element(X1,powerset(X0)) )
| ~ finite(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( finite(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> finite(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(f269,plain,
! [X0] :
( ~ in(X0,sK4(X0))
| in(relation_image(sK3,sK4(X0)),sK2) ),
inference(resolution,[],[f124,f163]) ).
fof(f268,plain,
! [X0] :
( ~ in(sK2,relation_image(sK3,sK4(X0)))
| in(sK4(X0),X0) ),
inference(resolution,[],[f124,f163]) ).
fof(f265,plain,
! [X0] :
( ~ in(X0,sK4(X0))
| in(sK4(X0),powerset(relation_dom(sK3))) ),
inference(resolution,[],[f123,f163]) ).
fof(f264,plain,
! [X0] :
( ~ in(powerset(relation_dom(sK3)),sK4(X0))
| in(sK4(X0),X0) ),
inference(resolution,[],[f123,f163]) ).
fof(f267,plain,
~ in(powerset(relation_dom(sK3)),sK4(powerset(relation_dom(sK3)))),
inference(resolution,[],[f266,f163]) ).
fof(f266,plain,
in(sK4(powerset(relation_dom(sK3))),powerset(relation_dom(sK3))),
inference(factoring,[],[f123]) ).
fof(f146,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f261,plain,
! [X0] :
( ordinal(sK7(X0))
| ~ ordinal(powerset(X0)) ),
inference(resolution,[],[f137,f153]) ).
fof(f137,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ( ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1) )
| ~ element(X1,X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( element(X1,X0)
=> ( ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_arytm_3) ).
fof(f241,plain,
! [X0] :
( ~ ordinal(powerset(X0))
| epsilon_connected(sK7(X0)) ),
inference(resolution,[],[f136,f153]) ).
fof(f224,plain,
! [X0] :
( ~ ordinal(powerset(X0))
| epsilon_transitive(sK7(X0)) ),
inference(resolution,[],[f135,f153]) ).
fof(f136,plain,
! [X0,X1] :
( ~ element(X1,X0)
| epsilon_connected(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f221,plain,
( epsilon_transitive(sK2)
| ~ ordinal(powerset(powerset(sK1))) ),
inference(resolution,[],[f135,f120]) ).
fof(f135,plain,
! [X0,X1] :
( ~ element(X1,X0)
| epsilon_transitive(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f129,plain,
! [X0] :
( element(sK6(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0] :
( ( finite(sK6(X0))
& ~ empty(sK6(X0))
& element(sK6(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f50,f81]) ).
fof(f81,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK6(X0))
& ~ empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(f127,plain,
! [X0] :
( element(sK5(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ( ~ empty(sK5(X0))
& element(sK5(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f49,f79]) ).
fof(f79,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f163,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f147,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f220,plain,
! [X0] :
( function(relation_dom(X0))
| ~ empty(X0) ),
inference(resolution,[],[f144,f139]) ).
fof(f155,plain,
! [X0] : element(sK8(X0),powerset(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( finite(sK8(X0))
& ordinal(sK8(X0))
& epsilon_connected(sK8(X0))
& epsilon_transitive(sK8(X0))
& function(sK8(X0))
& relation(sK8(X0))
& empty(sK8(X0))
& element(sK8(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f43,f85]) ).
fof(f85,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK8(X0))
& ordinal(sK8(X0))
& epsilon_connected(sK8(X0))
& epsilon_transitive(sK8(X0))
& function(sK8(X0))
& relation(sK8(X0))
& empty(sK8(X0))
& element(sK8(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
! [X0] :
? [X1] :
( finite(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f40]) ).
fof(f40,plain,
! [X0] :
? [X1] :
( finite(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& one_to_one(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f3]) ).
fof(f3,axiom,
! [X0] :
? [X1] :
( finite(X1)
& natural(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& one_to_one(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).
fof(f153,plain,
! [X0] : element(sK7(X0),powerset(X0)),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0] :
( empty(sK7(X0))
& element(sK7(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f28,f83]) ).
fof(f83,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK7(X0))
& element(sK7(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f145,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f219,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_dom(X0)) ),
inference(resolution,[],[f144,f140]) ).
fof(f144,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f131,plain,
! [X0] :
( finite(sK6(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f130,plain,
! [X0] :
( ~ empty(sK6(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f128,plain,
! [X0] :
( ~ empty(sK5(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f143,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f142,plain,
! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f141,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f213,plain,
! [X0] : relation(sK7(X0)),
inference(resolution,[],[f140,f154]) ).
fof(f215,plain,
relation(sK15),
inference(resolution,[],[f140,f175]) ).
fof(f140,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f207,plain,
! [X0] : function(sK7(X0)),
inference(resolution,[],[f139,f154]) ).
fof(f210,plain,
function(sK21),
inference(resolution,[],[f139,f191]) ).
fof(f209,plain,
function(sK15),
inference(resolution,[],[f139,f175]) ).
fof(f139,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f138,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( empty(X0)
=> finite(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
fof(f162,plain,
! [X0] : finite(sK8(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f161,plain,
! [X0] : ordinal(sK8(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f160,plain,
! [X0] : epsilon_connected(sK8(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f159,plain,
! [X0] : epsilon_transitive(sK8(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f158,plain,
! [X0] : function(sK8(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f157,plain,
! [X0] : relation(sK8(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f156,plain,
! [X0] : empty(sK8(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f154,plain,
! [X0] : empty(sK7(X0)),
inference(cnf_transformation,[],[f84]) ).
fof(f126,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f205,plain,
function(sK25),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
( function(sK25)
& empty(sK25)
& relation(sK25) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f19,f118]) ).
fof(f118,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK25)
& empty(sK25)
& relation(sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f204,plain,
empty(sK25),
inference(cnf_transformation,[],[f119]) ).
fof(f203,plain,
relation(sK25),
inference(cnf_transformation,[],[f119]) ).
fof(f202,plain,
ordinal(sK24),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
( ordinal(sK24)
& epsilon_connected(sK24)
& epsilon_transitive(sK24)
& empty(sK24)
& function(sK24)
& relation(sK24) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f45,f116]) ).
fof(f116,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(sK24)
& epsilon_connected(sK24)
& epsilon_transitive(sK24)
& empty(sK24)
& function(sK24)
& relation(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f15]) ).
fof(f15,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(f201,plain,
epsilon_connected(sK24),
inference(cnf_transformation,[],[f117]) ).
fof(f200,plain,
epsilon_transitive(sK24),
inference(cnf_transformation,[],[f117]) ).
fof(f199,plain,
empty(sK24),
inference(cnf_transformation,[],[f117]) ).
fof(f198,plain,
function(sK24),
inference(cnf_transformation,[],[f117]) ).
fof(f197,plain,
relation(sK24),
inference(cnf_transformation,[],[f117]) ).
fof(f196,plain,
function(sK23),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
( function(sK23)
& relation(sK23) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f44,f114]) ).
fof(f114,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK23)
& relation(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f9]) ).
fof(f9,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f195,plain,
relation(sK23),
inference(cnf_transformation,[],[f115]) ).
fof(f194,plain,
function(sK22),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
( function(sK22)
& relation(sK22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f36,f112]) ).
fof(f112,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK22)
& relation(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f36,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f193,plain,
relation(sK22),
inference(cnf_transformation,[],[f113]) ).
fof(f192,plain,
relation(sK21),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
( relation(sK21)
& empty(sK21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f21,f110]) ).
fof(f110,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK21)
& empty(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f21,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f191,plain,
empty(sK21),
inference(cnf_transformation,[],[f111]) ).
fof(f190,plain,
ordinal(sK20),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
( ordinal(sK20)
& epsilon_connected(sK20)
& epsilon_transitive(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f14,f108]) ).
fof(f108,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK20)
& epsilon_connected(sK20)
& epsilon_transitive(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f14,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f189,plain,
epsilon_connected(sK20),
inference(cnf_transformation,[],[f109]) ).
fof(f188,plain,
epsilon_transitive(sK20),
inference(cnf_transformation,[],[f109]) ).
fof(f187,plain,
relation(sK19),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
( relation(sK19)
& ~ empty(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f23,f106]) ).
fof(f106,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK19)
& ~ empty(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f186,plain,
~ empty(sK19),
inference(cnf_transformation,[],[f107]) ).
fof(f185,plain,
ordinal(sK18),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
( ordinal(sK18)
& epsilon_connected(sK18)
& epsilon_transitive(sK18)
& ~ empty(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f42,f104]) ).
fof(f104,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK18)
& epsilon_connected(sK18)
& epsilon_transitive(sK18)
& ~ empty(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
inference(pure_predicate_removal,[],[f4]) ).
fof(f4,axiom,
? [X0] :
( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(f184,plain,
epsilon_connected(sK18),
inference(cnf_transformation,[],[f105]) ).
fof(f183,plain,
epsilon_transitive(sK18),
inference(cnf_transformation,[],[f105]) ).
fof(f182,plain,
~ empty(sK18),
inference(cnf_transformation,[],[f105]) ).
fof(f181,plain,
ordinal(sK17),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
( ordinal(sK17)
& epsilon_connected(sK17)
& epsilon_transitive(sK17)
& ~ empty(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f16,f102]) ).
fof(f102,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK17)
& epsilon_connected(sK17)
& epsilon_transitive(sK17)
& ~ empty(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f16,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f180,plain,
epsilon_connected(sK17),
inference(cnf_transformation,[],[f103]) ).
fof(f179,plain,
epsilon_transitive(sK17),
inference(cnf_transformation,[],[f103]) ).
fof(f178,plain,
~ empty(sK17),
inference(cnf_transformation,[],[f103]) ).
fof(f177,plain,
finite(sK16),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
( finite(sK16)
& ~ empty(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f5,f100]) ).
fof(f100,plain,
( ? [X0] :
( finite(X0)
& ~ empty(X0) )
=> ( finite(sK16)
& ~ empty(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f5,axiom,
? [X0] :
( finite(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f176,plain,
~ empty(sK16),
inference(cnf_transformation,[],[f101]) ).
fof(f175,plain,
empty(sK15),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
empty(sK15),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f29,f98]) ).
fof(f98,plain,
( ? [X0] : empty(X0)
=> empty(sK15) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f174,plain,
~ empty(sK14),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
~ empty(sK14),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f30,f96]) ).
fof(f96,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK14) ),
introduced(choice_axiom,[]) ).
fof(f30,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f342,plain,
~ spl26_7,
inference(avatar_contradiction_clause,[],[f341]) ).
fof(f341,plain,
( $false
| ~ spl26_7 ),
inference(global_subsumption,[],[f206,f170,f121,f122,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f192,f193,f194,f195,f196,f197,f198,f199,f200,f201,f202,f203,f204,f205,f126,f154,f156,f157,f158,f159,f160,f161,f162,f120,f138,f139,f209,f210,f207,f140,f215,f213,f141,f142,f143,f128,f130,f131,f144,f219,f145,f153,f155,f220,f147,f163,f127,f129,f135,f221,f136,f224,f241,f137,f261,f146,f123,f266,f267,f124,f264,f265,f268,f269,f132,f270,f273,f271,f222,f164,f223,f239,f240,f259,f260,f243,f245,f165,f166,f167,f168,f169,f295,f296,f286,f288,f290,f292,f125,f303,f172,f306,f307,f308,f305,f314,f315,f312,f313,f309,f316,f317,f171,f321,f322,f323,f324,f320,f328,f335,f334,f339,f340]) ).
fof(f333,plain,
( spl26_7
| spl26_8 ),
inference(avatar_split_clause,[],[f320,f330,f326]) ).
fof(f283,plain,
( ~ spl26_5
| spl26_6 ),
inference(avatar_split_clause,[],[f270,f280,f276]) ).
fof(f276,plain,
( spl26_5
<=> finite(powerset(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_5])]) ).
fof(f280,plain,
( spl26_6
<=> finite(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_6])]) ).
fof(f255,plain,
( ~ spl26_3
| ~ spl26_4
| spl26_1 ),
inference(avatar_split_clause,[],[f236,f227,f252,f248]) ).
fof(f248,plain,
( spl26_3
<=> epsilon_transitive(powerset(powerset(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_3])]) ).
fof(f252,plain,
( spl26_4
<=> epsilon_connected(powerset(powerset(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_4])]) ).
fof(f227,plain,
( spl26_1
<=> ordinal(powerset(powerset(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_1])]) ).
fof(f236,plain,
( ~ epsilon_connected(powerset(powerset(sK1)))
| ~ epsilon_transitive(powerset(powerset(sK1)))
| spl26_1 ),
inference(resolution,[],[f229,f147]) ).
fof(f229,plain,
( ~ ordinal(powerset(powerset(sK1)))
| spl26_1 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f234,plain,
( ~ spl26_1
| spl26_2 ),
inference(avatar_split_clause,[],[f221,f231,f227]) ).
fof(f231,plain,
( spl26_2
<=> epsilon_transitive(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_2])]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU297+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 11:20:51 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (11619)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (11622)WARNING: value z3 for option sas not known
% 0.14/0.37 % (11620)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (11621)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (11623)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (11622)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (11626)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37 % (11625)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 % (11624)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.39 % (11622)First to succeed.
% 0.14/0.39 % (11622)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-11619"
% 0.14/0.39 % (11622)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.40 % (11622)------------------------------
% 0.21/0.40 % (11622)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.40 % (11622)Termination reason: Refutation
% 0.21/0.40
% 0.21/0.40 % (11622)Memory used [KB]: 1043
% 0.21/0.40 % (11622)Time elapsed: 0.023 s
% 0.21/0.40 % (11622)Instructions burned: 34 (million)
% 0.21/0.40 % (11619)Success in time 0.046 s
%------------------------------------------------------------------------------